On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

TL;DR

This paper proves that one-dimensional random Schrödinger operators with certain decaying matrix-valued potentials almost surely have an interval of purely absolutely continuous spectrum, extending previous results and providing a new proof.

Contribution

It introduces a new proof and generalizes existing results on the ac spectrum of 1D random Schrödinger operators with matrix-valued potentials.

Findings

Almost sure existence of an ac spectrum interval

Applicable to Schrödinger operators on a strip

Generalizes previous results by Delyon, Simon, and Souillard

Abstract

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.